I remain fairly confident that despite the craze surrounding Hamilton, it will not be enough to significantly raise the number of viewers. While Hamilton is exciting, the season at large is indeed a typical season. Other than Hamilton being a cultural juggernaut, nothing else causes this season to stand out any more than seasons past. We have had cultural juggernauts before. Rent, for example, was huge at the time, but not so huge enough to make new people sit through an awards ceremony on TV.
You also have to take into account the popularity of cord cutting. Many people are ditching traditional broadcast TV, and will watch highlights on social media, others will wait until it is available on Hulu or Amazon.
At the end of the day, I don't suspect that viewership will be much higher than 6 to 7 million. Time will tell, but I certainly wouldn't be placing any bets that you will see higher numbers.